Introduction

This study estimated the effect of receiving help during a disaster on subsequent cooperation for a common-pool resource. This chain of altruism is called generalized exchange emerged by upstream indirect reciprocity, based on the exchange theory and cooperation theory [1,2,3]. Theoretical studies on upstream indirect reciprocity have found evidence of its importance in understanding human cooperation in society [4,5,6]. However, there are few empirical analyses on it in real-life settings (not in laboratories) because of the difficulty in establishing cause and effect. This paper attempted to estimate the impact of receiving help on subsequent cooperation through a quasi-experimental approach using big data.

This paper focused on cooperation for an online common-pool resource called “Free Tank” in “mineo”, a mobile communication service in Japan. Free Tank is a packet-sharing system among mineo users. They can share their unused monthly mobile data by putting them into Free Tank. The data in Free Tank are basically available for all members. In addition to such normal use, Free Tank has a special support system to provide support to disaster-stricken members in getting mobile data. This study’s analysis estimated the effect of receiving this special support on the subsequent cooperation with Free Tank. The data of Free Tank accurately recorded the members’ online cooperative behavior. Thus, it was quite a suitable method for a study on human cooperation in society, enabling us to analyze causal relationships between chains of cooperative behavior.

In addition, this paper had a twofold contribution. One was the study on helping behavior during natural disasters, and the other was the study of online sharing systems. It has been reported that various types of helping behavior play an important role in the aftermath of natural disasters [7]. In recent times, moreover, the importance of informational support for disaster victims has been emphasized and recognized as an administrative issue [8]. During a natural disaster, victims require information on where to get water, food and fuel, where they will be safe, and how to get to the evacuation centers. In addition, they also need to get in touch with family and friends to confirm their safety. For this purpose, they use television, radio, Internet, and mobile communication service. These days, people get much of their information through the Internet [8]. However, in disaster areas, there are many cases where the victims cannot use Wi-Fi and have to rely on mobile communication. A strong capacity for mobile communication is then required because the usual monthly package allocation may be exceeded. Thus, it has recently been common for mobile phone companies to provide disaster victims with data for free [9, 10]. This paper gives insight into the importance and effect of such informational support. In addition, this analysis may provide a better understanding of the role of some kind of online sharing system and helping behavior in online communities.

Related literature

Natural disasters and altruistic behavior

Although this paper focused on altruistic behavior and natural disasters, there have been several studies on related themes, such as who engages in disaster relief volunteer work [11,12,13,14,15] and what kind of disaster victims receive help during natural disasters [16,17,18,19,20]. These studies analyzed the effect of age, educational level, socioeconomic status, past behavior, and social network on doing and receiving help. Another line of research is on the impact of receiving help during natural disasters on subsequent altruistic behavior [21,22,23]. Atsumi [21] reported the phenomenon called “disaster area relay”, which means that disaster victims who had received help, in turn, also helped other disaster victims in succeeding disasters. This happened among disaster relief volunteers during the Great Hanshin-Awaji Earthquake (1995 in Japan) and the Great East Japan Earthquake (2011 in Japan), and other natural disasters. Similarly, Mitani [23] found that people who had been helped by disaster relief volunteers also tended to engage in disaster relief volunteer work themselves in subsequent disasters. This was measured through survey data in Japan.

The disaster area relay is characterized as giving back to third parties, not to the people who helped them [23]. Such giving back to third parties is called generalized exchange [1, 2]. Generalized exchange has been one of the central topics in classical social exchange theory [24,25,26]. It has been conceived as one of the mechanisms that enhance social solidarity [2, 27].Footnote 1

The other aspect of disaster area relay is that it emerges from indirect reciprocity.Footnote 2 There are two types of reciprocity: direct reciprocity and indirect reciprocity. In the former case, person A helps the other person B, and then person A is reciprocated by person B directly. In the latter case, reciprocation is not by person B but by someone else. In addition, evolutionary biology studies on indirect reciprocity distinguish between downstream and upstream indirect reciprocity. The former means that a person who has helped in the past has a higher chance of receiving help [29,30,31,32,33,34,35,36,37,38,39], while the latter means that a person who has just received help will help someone as well. Many studies have found that downstream indirect reciprocity can be maintained by reputation-based interaction [39,40,41]. On the other hand, upstream indirect reciprocity is said to be harder to understand from an evolutionary perspective [3] because, in this exchange, resource giving is not based on the reputation of the recipients; even “free riders” can then benefit easily. Conditions to maintain upstream indirect reciprocity have been found to be limited: in small groups [4], in combination with group-leaving strategies [5], or on a one-dimensional lattice in connection with direct reciprocity [6].

In sum, disaster area relay corresponds to generalized exchange by upstream indirect reciprocity.Footnote 3 In disaster area relay, a disaster victim is helped by the disaster relief volunteers, and after that, he/she—as one of disaster relief volunteers—helps a disaster victim. Such subsequent help is not because of the victim’s reputation but because of receiving help in the past. Thus, disaster area relay is characterized as helping behavior to third parties that emerges from receiving help in the past.

Empirical evidence on upstream indirect reciprocity

Upstream indirect reciprocity has only been observed in controlled experimental settings, and there is little evidence of it in real-world environments [42,43,44,45,46,47,48]. Firstly, because the conditions for maintaining upstream indirect reciprocity are limited, as theoretical studies have found [4,5,6]. Secondly, proving a causal relationship between receiving help and subsequent helping behavior is difficult. Experimental studies have revealed strong causal evidence between receiving help and giving back to third parties, demonstrating internal validity. However, they have not been able to guarantee that upstream indirect reciprocity can be observed in a real-world environment; that is, they lack external validity.Footnote 4

On the other hand, the disaster area relay is a valuable example of upstream indirect reciprocity in society. Disaster studies have shown that this can actually be observed in society, demonstrating the external validity of indirect reciprocity. However, observational studies, including in-depth interviews and quantitative research, have limitations in proving causality. They have external validity but not internal validity.

Therefore, a study with both internal validity and external validity is required. This means that a causal analysis with data from actual events is required. This paper attempted such a causal analysis with data on helping behaviors in a real setting. These data include giving data traffic (packets) to disaster victims and their subsequent behaviors in mineo. This paper investigated the causal relationship through the difference-in-difference estimator (hereafter DID).

Description of the case

This paper focused on upstream indirect reciprocity in mineo, one of the MVNOs (mobile virtual network operators) in Japan. Mineo provides disaster victims with packets (data allocation in mobile phone service) called “Disaster Relief Tank”, which is one way to use Free Tank. These are further explained below.

Mineo and Free Tank

Mineo is a mobile communication service provided by OPTAGE Inc., and it has been one of the MVNOs (mobile virtual network operators) in Japan since 2014. Mineo’s Free Tank is a packet-sharing system among members who can use the monthly contracted amount of data. Free Tank is located in mineo-KINGDOM, an online community among mineo users. If members have unused data in a month, they can carry it forward only to the next month. Beyond that term, the unused data will expire. However, members can put it into the Free Tank before the expiration date to keep it available. This action is called “Tank-in”.

The data a member puts into the Free Tank can be used by other members who run out of data that month. This action is called “Tank-out”. Thus, Free Tank is an online packet-sharing system among mineo-KINGDOM members. Since it is available to all members, it is a common-pool resource for the members. Thus, Free Tank can be maintained by members’ cooperation. However, cooperation does not come at a tangible cost but an intangible cost. Members have to log in to mineo-KINGDOM and put the proper amount of data into Free Tank. It is so cumbersome that some members have requested the company to create a system that enables members to automatically put almost expiring data into Free Tank.Footnote 5 Therefore, there is the possibility that members put nothing in and yet get as much as they can. This would lead to the depletion crisis, which is a social dilemma problem [55,56,57]. Free Tank did face this crisis twice (Fig. 1). As a result, some regulations regarding Tank-out have been established, one of which is that members can only obtain data out of Free Tank up to 1 GB from the 21st to the last day of every month [58].

Fig. 1
figure 1

Stock of Free Tank [59]. The vertical axis represents the remaining amount of data (TB) in Free Tank

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Disaster Relief Tank

Disaster Relief Tank, which allows disaster victims to take up to 10 GB of data out of Free Tank at any time, is less limited than the regular Tank-out system. Disaster victims are those whose contracted area (located with GPS) is in the place where the disaster relief act is applied. The disaster relief act is one of the acts in Japan and it applies to areas where natural disasters have caused significant damage to both humans and houses. By implementing this act, affected local governments will be able to request rescue from the self-defense forces and the Japanese Red Cross Society and will be able to receive material and human assistance quickly.

Disaster Relief Tank can be considered as helping by mineo-KINGDOM members as a whole because Free Tank is based on their cooperation. How does such help from other members affect the following behavior of the disaster victims? If they contributed to Free Tank after having received help during a natural disaster, it can be considered as generalized exchange emerged by upstream indirect reciprocity, in the sense that the disaster victims had received help unconditionally, and they then gave back to those who were not necessarily the ones who had helped them.Footnote 6 The benefits of Disaster Relief Tank are not based on a member’s reputation.

In fact, some disaster victims considered their reciprocation as not for the members but for the system or mineo, saying thankful comments like “Thank you, mineo”. Nevertheless, their donation to their common-pool resource can help other members that are not the ones who had helped them, that is, third parties, in the future. In this sense, their contribution is for third parties. Therefore, Disaster Relief Tank has the features of generalized exchange between an individual and a group.

This paper focused on the effect of receiving help during a natural disaster on a person’s subsequent cooperation for a common-pool resource—whether having received help during a natural disaster increased the subsequent contribution to the common-pool resource or not. Does upstream indirect reciprocity work in society, contrary to the findings of the theoretical studies? This paper investigated this research question using the data on the activities of mineo-KINGDOM members. These data included the exact timing of all members’ activities (Tank-in, Tank-out, and Disaster Relief Tank), which enabled us to identify the causal relationship between receiving help during a natural disaster and the subsequent provision of help by individuals. Difference-in-difference estimation was applied to the causal analysis in this paper, and it had both external validity and internal validity.

Data

Natural disasters and the Disaster Relief Tank

The following analysis used the data provided by OPTAGE Inc. These data are action records (6,008,226 cases) of mineo-KINGDOM members from December 2015 to December 2018. Each case has the following information: user name, type of action (Tank-in/Tank-out/Disaster Relief Tank), amount of data, date, and comments. These highly granulated data inform us exactly who did what and when, and what they thought during Tank-in or Tank-out.

From December 2015 to December 2018, six natural disasters hit Japan: the 21st typhoon in October 2017, heavy snow in February 2018, the Osaka earthquake in June 2018, the west Japan torrential rainfall in July 2018, heavy rain in September 2018, and the Hokkaido earthquake in September 2018. Table 1 shows the summary of the damage situations of these natural disasters. The “Area” in the third column indicates the prefectures covered by the Disaster Relief Act. As this table shows, damage caused by heavy snowfall and earthquakes tended to be concentrated in a few prefectures, while damage caused by heavy rain and floods tended to be widespread in many prefectures. In these areas, many people were killed, many houses were seriously damaged, and infrastructure was destroyed in many areas. Based on the Disaster Relief Act, victims in these disaster areas could receive various public services.

Table 1 Damage caused by six natural disasters
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Table 2 shows information on six natural disasters and Disaster Relief Tank usage. The “available period” in this table means the period in which Disaster Relief Tank was available for victims in mineo. These periods were later than when the natural disasters occurred, and the Disaster Relief Act was then applied. Thus, the number of cases that availed of Disaster Relief Tank exceeded the number of its users. The periods of heavy rain and the Hokkaido earthquake (the bottom two rows of the table) overlapped, and it was impossible to distinguish which disaster the users suffered from. Thus, two natural disasters were merged as one event in the following analysis.

Table 2 Natural disasters and usage of the Disaster Relief Tank
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It is important to note that the victims here are those who used Disaster Relief Tank. Thus, the terms “victims” and “users of Disaster Relief Tank” are used interchangeably here. Of course, more members had suffered from the six natural disasters, but we cannot fully capture all of them. We do not have the data on which members suffered from them, but we have the data on which members used Disaster Relief Tank. Therefore, the victims referred to here are members who suffered from one of the six natural disasters and received help from Disaster Relief Tank. This distinction is important in the treatment of DID. This issue is discussed in detail in the following section.

Figure 2 shows how much data victims received from Disaster Relief Tank. The left-hand side shows the histogram of the data received per case, while the right-hand side shows the histogram of the data received per victim. Some victims received small amounts of data at a time, but many eventually received the maximum amount of data (10 GB).

Fig. 2
figure 2

Histograms of usage of Disaster Relief Tank. Left: histogram per case, 17,343 cases, mean is 5751.19 MB, the standard deviation is 3902.04 MB. Right: histogram per person, 13,409 people, mean is 7418.85 MB, standard deviation is 3616.82 MB

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Method

Difference-in-difference estimator

To analyze the causal relationship between receiving help during a natural disaster and subsequent helping behavior, this paper used difference-in-differences (DID). DID is one of the most commonly used methods for identifying causal effects in applied microeconomics research because it only requires four types of data from at least two treatment groups (units receiving treatment and units never receiving treatment) and two discrete time periods (pre- and post-treatment).

The estimand of DID is the average treatment effect on the treated (ATT). To formalize this, we denoted \({Y}_{i,t}(1)\) as the value of the outcome of interest for unit \(i\) in period \(t\) when the unit received treatment and \({Y}_{i,t}(0)\) as the outcome for unit \(i\) in period \(t\) when it did not receive treatment. The average treatment effect (\(\delta\)) is defined as the average difference \({Y}_{i,t}\left(1\right)-{Y}_{i,t}\left(0\right)\) across the population.

However, \({Y}_{i,t}(1)\) and \({Y}_{i,t}(0)\) cannot be observed at the same time. This is called the “fundamental problem of causal inference” [67]. The basic idea behind DID designs is to impute the counterfactual outcomes using the observed outcomes of treatment and control units. In particular, DID assumes that the observed trend in the outcome variable from period \(t=0\) to \(t=1\) in the control units is the same as the trend in the treatment units if they had not received treatment. Under this parallel trend assumption, the treatment effect on the treated can be estimated using the observed treatment–control unit difference in the pre- and post-treatment differences in the outcome:

$$\delta \equiv \mathrm{E}\left[{Y}_{T,1}\left(1\right)-{Y}_{T,1}\left(0\right)\right]=\mathrm{E}\left[\left\{{Y}_{T,1}\left(1\right)-{Y}_{T,0}\left(1\right)\right\}-\left\{{Y}_{T,1}\left(0\right)-{Y}_{T,0}\left(0\right)\right\}\right]$$
$$=\mathrm{E}\left[\left\{{Y}_{T,1}\left(1\right)-{Y}_{T,0}\left(1\right)\right\}-\left\{{Y}_{C,1}\left(0\right)-{Y}_{C,0}\left(0\right)\right\}\right],$$

where \(T\) denotes treatment units and \(C\) denotes control units.

The first equality defined the estimand of interest but could not be directly estimated in the data. The second equality is followed by adding and subtracting \({Y}_{T,0}\left(0\right)\) and \({Y}_{T,1}\left(0\right)\). They are equal under the no-anticipation assumption but could not be directly estimated in the data because we did not observe \({Y}_{T,1}\left(0\right)-{Y}_{T,0}\left(0\right)\). The final equality followed the parallel trend assumption and was estimated in the data. This means that in the 2 × 2 design, the effect of the treatment on the outcome of interest was estimated empirically by comparing the change in the average outcome in the treated units to the change in the average outcome in the control units.

In practice, DID estimates are obtained through linear regression. As noted in the 2 × 2 DID, it can be considered as a fixed effects estimator [68].

$$y_{{{\text{it}}}} = \alpha + \beta_{1} {\text{TREAT}}_{i} + \beta_{2} {\text{POST}}_{t} + \delta \left( {{\text{TREAT}}_{i} \cdot {\text{POST}}_{t} } \right) + \varepsilon_{{{\text{it}}}}$$
(1)

where \({\mathrm{TREAT}}_{i}\) is an indicator variable for the treated unit and \({\mathrm{POST}}_{t}\) is an indicator variable for observations in periods \(t=1\). The advantage of the regression analysis was that it provided a point estimate for \(\delta\) with standard errors and enabled us to add control variables [68]. In addition, it made it easy to extend to more than two units and two time periods. The staggered DID regression model took the following two-way fixed effects form:

$$y_{{{\text{it}}}} = \alpha_{i} + \lambda_{t} + \delta D_{{{\text{it}}}} + \varepsilon_{{{\text{it}}}}$$
(2)

where \({\alpha }_{i}\) is unit fixed effects and \({\lambda }_{t}\) is time fixed effects, and \({D}_{it}={\mathrm{TREAT}}_{i}\bullet {\mathrm{POST}}_{t}\) is an indicator for a treated unit in treated periods. In a baseline model, it represents a weighted average of all possible 2 × 2 DID estimators [69].

Both analyses were conducted. First, the 2 × 2 DID for each of the five natural disasters was conducted. The change in the average outcome in the treated units was compared with the change in the average outcome in the control units through a Welch’s t-test. Since heterogeneity and the dynamic change of ATT may cause a biased estimate of \(\delta\) [70], this had to be checked. Second, the two-way fixed effects model was analyzed to control covariates. The 6,008,226 action records were changed into monthly action data, which contained 6,008,226 observations. Specifically, there were 37 time periods (2015/12 ~ 2018/12) and 295,491 members. Since each member joined and left mineo at different times, the months when a member was absent were missing values. Thus, this was unbalanced panel data.

One method for dealing with heterogeneity and the dynamic change of ATT is the Callaway and Sant’Anna estimator [71]. However, the data in this paper were not fit for this method. The number of victims of the first two natural disasters was insufficient for estimation. Moreover, the Tank-in activities of each member fluctuated from month to month. Thus, the method which estimates per treatment unit and period is not fit for this data.

Assignment and treatment

In the DID design, the assumptions mentioned above were crucially important to identify causality. In order to hold these assumptions, previous research often used natural phenomena (e.g., weather and natural disaster) as an exogenous random shock [20, 72]. If units are divided into the treated and control groups by a random shock, they can be seen as being randomly assigned.

In this paper, natural disasters are used as a random device. However, it is important to ensure that the causal relationship of interest is not between suffering from a natural disaster and subsequent helping behavior, but between receiving help during a natural disaster (using the Disaster Relief Tank) and subsequent helping behavior. We did not have the data on who the victims were (assignment), but rather on the victims who used Disaster Relief Tank (treatment). Suffering from a natural disaster is a random shock, while using Disaster Relief Tank is not. Thus, assignment and treatment seemed to have a gap.

To solve this, we established that the assignment was comprised of those who had “seriously” suffered from a natural disaster, not automatically everyone in a disaster area. Unlike the Disaster Relief Act, which covers everything in a proclaimed disaster area, we narrowed the concept to victims who had houses (partly) ruined or flooded, infrastructures that were shut down, and those forced to go to an evacuation shelter.

This assumption also solved the empirical problem. The members who seriously suffered from a natural disaster (= randomly assigned to the treatment group) were considered to always use the Disaster Relief Tank (= received treatment). This assumption is not unrealistic. According to the Ministry of Internal Affairs and Communication [8], a few days after the Great East Japan Earthquake, the amount of communication traffic using mobile data in the disaster areas was about four times larger than during normal times. The data traffic, including mobile data (3 GB) and Wi-Fi communication (15 GB), is about 18 GB per month in Japan on average [73]. If accurate, people use 600 MB per day on average in normal times, and disaster victims use 2.4 GB (= 600 MB × 4) per day. Victims would require 16.8 GB a week for Wi-Fi. Eighty percent of contract data volumes of the mineo-KINGDOM members is below 3 GB [74].

Moreover, by this assumption, no one is in classification II in Table 3 because those assigned to the treatment group—those who experienced serious damage in a natural disaster, always used Disaster Relief Tank. The question was how many people were in classification III in Table 3. These people did not experience serious damage (= randomly assigned to the control group) but used Disaster Relief Tank. There may have been such people because all of the members in a disaster area who applied under the Disaster Relief Act had the right to use Disaster Relief Tank, no matter how much (or how little) damage they experienced. However, we presumed there were not so many people in classification III for two reasons. Firstly, most people who used Disaster Relief Tank got 10 GB. However, such an amount is not necessary for most of the members during normal times because 80% of the contract data volumes of the members is below 3 GB, as mentioned above. On the other hand, during a disaster, the victims require much more data. Secondly, most of Disaster Relief Tank users left grateful comments, and only a few left disrespectful ones (16 comments by eight users out of 17,343 comments). Except for such users, it is reasonable to think that most users had good reasons to use Disaster Relief Tank. Therefore, most of the members of mineo fell into classifications I or IV, that is, compliers, in Table 3. This means that the gap between assignment and treatment was small enough to assume a quasi-experiment setting. We will check whether this assumption is valid or not through data analysis in the following section.

Table 3 Assignment and treatment
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Result

2 × 2 DID design

We conducted a 2 × 2 difference-in-differences (DID) estimation for each natural disaster. We compared the change in the average contribution of the treated units to that of the control units using Welch’s t-test. Contribution refers to the difference between the sum of the amount of data of Tank-in and the sum of the amount of data of Tank-out (not including Disaster Relief Tank). Free Tank is a common-pool resource, so the amount of data that a member finally puts into Free Tank is considered as cooperation. This paper conceptualizes helping behavior (cooperation) as a contribution to Free Tank.

Figure 3 shows the average monthly contribution of victims and nonvictims for five natural disasters. The term “nonvictims” conceptually refer to those who were never treated. Specifically, “victims” refer to set I in Table 3, and nonvictims refer to set IV. The data we have are whether or not members used Disaster Relief Tank. Therefore, the former appears to correspond to sets I and III and the latter to sets II and IV. However, as discussed above, sets II and III are assumed to be quite small. Furthermore, for each disaster, the nonvictims must satisfy the condition of being a mineo member at the time the disaster occurred. Therefore, for example, the nonvictims of the first disaster (the 21st typhoon) would refer to the members who never used Disaster Relief Tank during any other disasters and who had joined mineo before October 21, 2017. Note that nonvictims of each natural disaster were a different set of members.Footnote 7

Fig. 3
figure 3

Contributions of victims and nonvictims. Dotted vertical lines represent the time periods of the natural disasters

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We can observe three important points in Fig. 3. Firstly, the trends of the contribution of both groups appear to be similar except for immediately after the natural disaster. This suggests that the parallel assumption, which is crucially important for DID, is valid. Secondly, the average monthly contributions among victims are generally lower than those of nonvictims before the disasters. This could be because some of the very cooperative members were not included as victims, as the number of victims is much smaller than that of nonvictims. However, it is also possible that victims are less cooperative than nonvictims. In other words, a large portion of group III in Table 3 could consist of victims. To account for this possibility, we will include the past amount and number of Tank-out as control variables in two-way fixed effects models to correct for selection bias later. Thirdly, the victims’ contributions dramatically increased immediately after the natural disaster. This could be because the data that the members obtained from Free Tank or Disaster Relief Tank expires at the end of the following month. Thus, there is a possibility that the data the victims were unable to use was returned in the following month. Conversely, since no data expire in the month after they put data into Free Tank, the likelihood of Tank-in decreases.

The spike in contributions immediately after the disaster does not mean that the help is useless for the victims. The following month’s spike is at most 3 GB, while most of the victims obtained 10 GB. Thus, they used more than 7 GB, approximately. This amount of data cannot be obtained in normal time, and this support during natural disasters is helpful for the victims. The impact of such next-month returns on subsequent helping behavior will be discussed in detail later. Moreover, this suggests that the assumption we discussed above is valid. As we calculated above, 7 GB is needed for victims during a natural disaster, while too much for ordinary members. Thus, presumably, those who obtained from Disaster Relief Tank more or less suffered from natural disasters and are in need of a significant amount of data. Therefore, it is reasonable to think the assumption that the size of group III in Table 3 is small is plausible.

We compared the contributions of victims to those of nonvictims for each natural disaster using Welch’s t-test. Table 4 shows the summary of the results. “Difference” in the table means the difference between the average contribution after the natural disaster and the average contribution before the natural disaster. “Difference-in-difference” in the table means the difference between the change in the victims’ contribution and in the nonvictims’ contribution. These values indicate that overall, victims tended to contribute more than nonvictims after a natural disaster. As a result of the test for equality of variance (Bartlett test), every pair of variances was not equal. Therefore, we conducted Welch’s t-test (one-sided). As a result, for all natural disasters, the alternative hypotheses that the change in the victims’ contribution is larger than that of the nonvictims’ contribution were significantly supported.

Table 4 Summary of the Welch’s t-test
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This table indicates that nonvictims exhibit a negative difference in all natural disasters. In fact, the average contribution of each member to Free Tank has continued to decrease over the years, despite an increase in the number of members. However, we need to conduct further research to determine the reasons behind this trend.

Two-way fixed effects model

Next, we estimated the effect of receiving help during a natural disaster using a two-way fixed effects model. The baseline model is Eq. (2). We considered individual-specific trends by adding some control variables to this baseline model: the cumulative number of Tank-in, cumulative number of Tank-out, cumulative amount of Tank-in, cumulative amount of Tank-out, cumulative number of receiving “nice” among the comments, and duration of the membership. The variables related to Tank-in and Tank-out represented the members’ monthly contract data, partly indicating their altruism or selfishness. Moreover, the variable duration of memberships represented a commitment to the mineo-KINGDOM community. These factors could affect the members’ contribution. Table 5 summarizes the statistics of these control variables and the objective variable (contribution).

Table 5 Summary statistics
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Table 6 shows the results of the two-way fixed effects models. Model 1 is the baseline model, and Model 2 adds all the control variables to Model 1. Both models include both treatment unit and time fixed effects, and robust standard errors are clustered at the treatment unit levels [75, 76]. The estimation was conducted using the R package “fixest” [77]. The coefficient of receiving help during a natural disaster is positive and statistically significant. This relationship does not change even when all control variables are included. Due to the gap between treatment and assignment as discussed above, there is a possibility that some of the “nonvictims” are included in the “victims” because they were originally uncooperative but gained the right to obtain data during a natural disaster and obtained it without needing to. However, the fact that controlling for uncooperativeness (amount and number of Tank-out) in the first place does not significantly change the results suggests that this bias is not so large. Therefore, receiving help from the Disaster Relief Tank was proven to increase subsequent helping behavior.

Table 6 Results of the two-way fixed effects model
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Mechanism of subsequent helping behavior

Figure 3 shows that the subsequent helping behavior of the victims dramatically increased immediately after the natural disaster, and after that, the amount of contribution stayed stable. This could be because the victims had taken the maximum amount of data (10 GB), but in the end, they did not use all of it and returned it the next month. However, this return does necessarily result from gratitude and indirect reciprocity.

We have to assess the impact of such next-month return. In order to prove that the effect of receiving help on subsequent help is not only due to such next-month return but also to indirect reciprocity, two additional analyses were conducted. One is DID without the “next month.” This analysis was to test whether the effect remains or not, even when the next-month return was removed. If the effect remained, it is proved that the subsequent helping behavior was not just caused by the next return. This analysis contributed to exclude the bias derived from the existence of group III in Table 3. Those in group III are defiers or always-takers who were assigned to the control group, that is, those who did not experience serious damage but they were treated used Disaster Relief Tank. As explained before, they would not have been able to use all 10 GB. If they returned a lot of data, it will be the next month. Therefore, DID without “next month” mitigated such bias.

The other analysis was to prove that receiving help during natural disasters increased the norm of indirect reciprocity. In the field of cultural anthropology and sociology, scholars have emphasized the significance of collective norms and solidarity as a mechanism for maintaining generalized exchange [1, 2, 27, 28, 78]. According to Atsumi [22], disaster victims who had received help felt a sense of debt, which they felt could be repaid by giving back to other victims (not necessarily the ones who had helped them) of future natural disasters. Willer and his coauthors found that generalized exchange increases group identity and solidarity compared to restricted exchange in a natural setting.Footnote 8 They hypothesized that group identity and solidarity would enhance cooperation, but they did not test it.

In addition, in the studies of upstream indirect reciprocity, it is assumed that gratitude is an emotion that can lead to upstream indirect reciprocity. A recipient of an altruistic act experiences gratitude and is more likely to help either the donor or another person. Thus, we have to confirm that receiving help leads to the emergence of the reciprocity norm. The causal relationship between receiving help during a natural disaster and the reciprocity norm was tested with DID. Originally, it was necessary to prove the mediation effect of the reciprocity norm between receiving help during a natural disaster and the subsequent helping behavior. However, it was difficult to estimate it by the panel data. Thus, the following DID provided indirect evidence of this mediation effect.

DID without next-month data

We conducted DID without the next month. In this analysis, data for the month in which the disaster occurred and the following month were excluded. For example, in the case of the 21st typhoon, which struck during 2017/10/31 ~ 11/13, a drastic increase in Tank-in occurred in December 2017. Therefore, we dropped the data for this month. Similarly, we dropped the data for March, July, September, and October 2018.

Table 7 represents the results of Welch’s t-test for each natural disaster. Each t-test was one-sided, and the alternative hypothesis was that the change in contributions of the victims was larger than that of nonvictims. As shown in this table, all of the difference-in-differences (except for the West Japan torrential rain) were smaller than those in Table 4, but they were still positive and statistically significant. Therefore, overall, receiving help during a natural disaster was still effective even when the effect of the next-month return was removed.

Table 7 Summary of the Welch’s t-test without next-month data
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Next, the effect of receiving help during a natural disaster was estimated using a two-way fixed effects model without next-month data. The procedure and control variables were the same as those of the two-way fixed effects model with full data. Table 8 shows that receiving help during a natural disaster still had a positive effect, although the effect size was smaller than that of the full data model. Therefore, receiving help during a natural disaster had a positive effect even without the next-month return, meaning that there is room for indirect reciprocity. This analysis dropped the next-month data of both victims and nonvictims. However, we also conducted an analysis in which we excluded the data of only the victims for the next month. This analysis came to the same conclusion.

Table 8 Results of two-way fixed effects model without next-month data
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The effect on the reciprocity norm

The next analysis shows that members’ comments that receiving help during a natural disaster increased the reciprocity norm. Obayashi and his colleagues analyzed comment data of mineo-KINGDOM users. They revealed by word2vec and cluster analysis that some comments included reciprocity norms [79]. The reciprocity norm consists of 22 words/phrases such as “mutual”, “each other”, “help each other”, “give and take”, “return”, “give back”, “borrow” and so on.

The model was a two-way fixed effects model with the same control variables as the previous analyses. The formula was

$$\mathrm{log}\left(\frac{P({Y}_{\mathrm{it}}=1)}{1-P({Y}_{\mathrm{it}}=1)}\right)={\alpha }_{i}+{\lambda }_{t}+\delta {D}_{\mathrm{it}}$$
(3)

where \({Y}_{\mathrm{it}}\) represented whether the member \(i\) used the words representing reciprocity norm in a month \(t\), and \(P({Y}_{\mathrm{it}}=1)\) represented the probability of that. Since fixed effects estimators of nonlinear panel data models have an incidental parameters problem that causes seriously biased estimation [80, 81], the estimation was conducted with an analytical bias correction using the R package “alpaca” [82, 83].

Table 9 shows the results of Model 1 and Model 2. In both models, receiving help during a natural disaster had positive effects that were statistically significant. When the cumulative number of Tank-out and Tank-in increases, the opportunity to leave grateful comments also increases. Thus, these variables should correlate with the usage of reciprocity-related words. However, even when these variables were included in the model, receiving help still had a positive effect. Therefore, receiving help during a natural disaster increased the odds ratio of using words representing the reciprocity norms.

Table 9 Results on the effects of receiving help on the reciprocity norm
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Conclusion and discussion

This paper discussed the relationship between receiving help and subsequent helping behavior. Previous works have reported that upstream indirect reciprocity works in laboratory settings. In addition, studies on disaster relief volunteers have reported the existence of “disaster area relay”. However, these works do not have either internal validity or external validity. In contrast, this paper shows that indirect reciprocity works in actual settings. The online common-pool resource, Free Tank, and natural disasters provided us with a natural experiment setting to identify the causality of receiving help to subsequent helping behavior. Causal inference with real-world data enabled us to prove the existence of upstream indirect reciprocity with both internal and external validity. In addition, observational studies on disaster area relays have focused on the chain between receiving help during a disaster and providing help during another disaster. In contrast, this paper focused on the chain between receiving help during a disaster and providing help not only during a disaster. In this sense, this paper provides broader evidence of the existence of upstream indirect reciprocity.

Theoretical and experimental studies have found that upstream indirect reciprocity is fragile and does not last for very long. Unfortunately, our analysis could not clarify this point because our data does not have enough periods after natural disasters. The fourth and fifth natural disasters only have two months of data after the disaster. This is a limitation of our data. Moreover, the spike in Tank-in immediately after the disaster and the rapid decrease are mainly caused by the feature of Free Tank system. Data can only be carried forward to the next month. Thus, the victims put a large amount of data into Free Tank in the month following the disaster. However, since the data can be carried over to the next month, it will not be added to Free Tank the month after putting it into Free Tank.

Despite these limitations, we revealed the existence of upstream indirect reciprocity as a mechanism of helping behaviors in natural settings. After all of the natural disasters we analyzed, upstream indirect reciprocity can be observed. This suggests that the propensity to help other people because of receiving help is robust in humans.

In a natural setting, the reciprocity norm probably plays an important role, as indicated by our additional analysis of the reciprocity norm. Willer found that generalized exchange enhances group identity and solidarity in an online community called Freecycle [27]. Our study is in line with their study. However, while Willer’s study used a survey to measure theoretical constructs, we were able to measure action in an exact manner using action and comment data. Thus, we clarified the causal relationship between exchange, action, and norms. This is a contribution of our study, but we were not able to compare it to other exchange structures. This requires further research.

The analyses also had some limitations. The first is related to assignment and treatment. We did not have the data on whether the members were assigned to the treatment group or not. Thus, we assumed that the set of type III in Table 3 is small. This assumption requires empirical verification in future research. However, if this assumption is not valid, our analyses would underestimate the impact of receiving help because uncooperative members would be included in the treatment group. Even so, the fact that it still had an effect is meaningful.

In conclusion, this paper provides evidence of the existence of upstream indirect reciprocity in natural settings. This finding has important implications for understanding the mechanisms of helping behavior and designing interventions to promote cooperation and prosociality.